Solving linear design problems using a linear-fractional value function

a r t i c l e i n f o Keywords: Decision analysis Multiple criteria analysis Linear-fractional preference structure Piecewise linear-fractional model Previous papers developed a method to easily elicit a decision maker's (DM) preferences and account for changes in the DM's preference structure. Those preferences are modeled by piecewise linear indifference curves with varying slopes producing a piecewise linear-fractional value function. Compared with traditional optimization problems which traditionally use cost minimization or revenue maximization, this model is DM-specific, it generates a knowledge set (KS) and allows the DM to find an optimal solution based on his/her expertise and preferences. When combined with real world constraints, maximizing the DM's preferences generates a decision support system (DSS) for solving specific organizational problems. This paper develops an efficient algorithm to solve a mathematical programming problem with a linear fractional objective function that models changing DM preferences and linear constraints. A DSS is developed and its algorithm is illustrated by constructing a specific example of the DSS for scheduling a police force when the objective is to maximize the police chief's expertise and preferences regarding law enforcement. In organizational decision problems firms have to assess their core objectives and the business processes needed to fulfill them [11]. When a decision maker (DM) is trying to solve a traditional problem such as profit maximization or cost minimization in products or services mix setting, the resulting model is often a linear decision problem and the solution is based on the weight of each attribute in the objective function which is determined by profit or cost parameters. Since most of these parameters are generally deterministic, the objective function is linear with constant rates of substitution. The solution is achieved by maximizing a linear profit function or minimizing a linear cost function while taking into account the relevant constraints. In this context, DM individual preferences, or other organizational preferences, are not necessarily included in the objective function although it may be beneficial to include them in the formulations of the problem. Moreover , there are even problems in which the objective function is not clearly defined because the problem is not strictly a problem of profit maximization or cost minimization. Those issues are highlighted by Bhatt and Zaveri [2]. They argue that decision support models should assist organizations in coping with specific challenges using their own specific knowledge and competencies. The purpose of this paper is …